Whenever the Zoning Board of Appeals, after hearing all the evidence presented upon an application for appeals under the provisions of this chapter, denies or rejects same, said Board may upon motion by any member of the Board hold a rehearing to review any order, decision or determination of the Board not previously reviewed. A unanimous vote of all members of the Board then present shall be required for such rehearing to occur. Such rehearing shall be subject to the same notice provisions as an original hearing. Upon such rehearing the Board may reverse, modify or annul its original order, decision or determination upon the unanimous vote of all members then present, provided that the Board finds that the rights vested in persons acting in good faith in reliance upon the reviewed order, decision or determination will not be prejudiced thereby.